Permuations and Combinations Problem

Can someone please explain the following question? I am also posting the solution but I didn't understand it well enough. Why is the answer (C)? Can someone explain it to me?

In a shooting competition, three targets are set as shown :

Condition :
Target (I) has four rings on which a person can hit in order from inside to outside.
Target (II) has three rings on which a person can hit in order from outside to inside.
Target (III) has five rings on which a person can hit in order from inside to outside.

The number of ways in which 12 shots (one at each ring) can be made :
[Hint : Any target can be chosen before not completing specific target but order of hit for a particular target should be as specified above in condition.]

Staff: Mentor

Okay, I think I got this now. Suppose one of the possible sequence of shots is-
AAAABBBCCCCC (Suppose we complete the disk fully which we started). Now the number of ways to arrange this word is 12!/(4!x3!x5!) or C(12,4) (select 4 places from the 12 above) x C(8,3) (select 3 places from the 8 left above now) x C(5,5) (select 5 places from the 5 left now)

Staff: Mentor

Okay, I think I got this now. Suppose one of the possible sequence of shots is-
AAAABBBCCCCC (Suppose we complete the disk fully which we started). Now the number of ways to arrange this word is 12!/(4!x3!x5!) or C(12,4) (select 4 places from the 12 above) x C(8,3) (select 3 places from the 8 left above now) x C(5,5) (select 5 places from the 5 left now)